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Observability analysis for structured bilinear systems: A graph-theoretic approach

“…Not so many works use the graph-theoretic approach to study nonlinear systems. The digraph we use in this paper is quite close to the one presented in [10]. The main differences are due to the fact that we adapt our representation to the context of observability analysis and to the fact that we deal with structured systems.…”

“…Figure 1, we represent the digraph associated to the SBLS defined by: As we can see, comparatively with the digraph presented in [10], the input vertices are removed since we study the state observability. Moreover, due to this removal, the edges, which start in [10] from the input vertices, start in our digraph from state vertices and constitute the A i -edges. Finally, as we are interested in structured systems, each edge represents a free parameter which has no numerical value.…”

“…Finally, as we are interested in structured systems, each edge represents a free parameter which has no numerical value. Thus, it is not necessary to indicate it on each edge of the digraph as in [10].…”

“…Unfortunately, not so many works based on graph-theoretic methods deal with nonlinear systems. Among them, [9,10] give conditions to the input-output decoupling and linearization of a nonlinear system, [15] gives sufficient conditions to fulfill the observability of bilinear systems and recently, [2] provides sufficient conditions for the uniform observability of some nonlinear systems. In this context, this paper is dedicated to the analysis of the observability for structured bilinear systems (SBLS).…”

Generic uniform observability analysis for bilinear systems

“…Unfortunately, few works based on graph-theoretic methods deal with nonlinear systems. Among them, (Svaricek, 1993) gives sufficient conditions to fulfill the observability of bilinear systems, (Lévine, 1997) study the input-output decoupling and linearization of a nonlinear system and more recently, (Bornard and Hammouri, 2002) proposes graphical sufficient conditions for checking the uniform observability of nonlinear systems which are preliminarily put in a canonical form. Finally, in we give a first analysis tool of the uniform observability condition.…”